Mathematics of CLIFFORD - A Maple package for Clifford and Grassmann algebras

TL;DR

CLIFFORD is a Maple package that facilitates advanced computations in Clifford and Grassmann algebras, supporting various algebraic structures and algorithms for the Clifford product.

Contribution

It introduces a versatile Maple package with two algorithms for Clifford product computation and supports multiple algebraic bases and properties.

Findings

Supports quaternion, octonion, and matrix computations in Clifford algebras.

Implements two algorithms: Chevalley's recursive and Rota-Stein sausage.

Discusses properties of reversion in different bases.

Abstract

CLIFFORD performs various computations in Grassmann and Clifford algebras. It can compute with quaternions, octonions, and matrices with entries in Cl(B) - the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B. Two user-selectable algorithms for Clifford product are implemented: 'cmulNUM' - based on Chevalley's recursive formula, and 'cmulRS' - based on non-recursive Rota-Stein sausage. Grassmann and Clifford bases can be used. Properties of reversion in undotted and dotted wedge bases are discussed.